The definition I’ve seen is the last common ancestor of procaryotes, eucaryotes, and archaea—which doesn’t strictly rule out the possibility of extinct domains whose existence we might infer.
And actually, there’s evidence of non-LUCA-descended organisms mentioned right in the paper: the other organisms that constituted the ecosystem of which LUCA was a part, whose existence (and some of whose characteristics) could be inferred from LUCA’s metabolism and immune system.